ALGORITHM READING NOTE

Binary Search

Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.

TYPEAlgorithmCATEGORYSearchDEPTHBeginnerTYPICAL COMPLEXITYO(log n)

SHORT INTERVIEW ANSWER

Start with this mental model

Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.

SIMPLE EXPLANATION

How it works, without unnecessary jargon

Compare target with the middle element.

If target is smaller, continue in the left half; if larger, continue in the right half.

EXECUTION

Read the algorithm as a sequence of decisions

Set left and right bounds.

Compute mid without leaving the range.

Move exactly one bound after each comparison until found or left > right.

A small example to keep in mind

Searching 23 in [3, 8, 12, 23, 31, 44] checks the middle, then keeps only the half where 23 can still exist.

READABLE JAVASCRIPT IMPLEMENTATIONJavaScript

function binarySearch(items, target) {
  let left = 0;
  let right = items.length - 1;

  while (left <= right) {
    const mid = left + Math.floor((right - left) / 2);
    if (items[mid] === target) return mid;
    if (items[mid] < target) left = mid + 1;
    else right = mid - 1;
  }
  return -1;
}

How to read this code

Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.

COMPLEXITY

O(log n)

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

WHEN TO USE IT

Good fit

Match the algorithm to the structure and preprocessing state of the data.

COMMON MISTAKES

What usually goes wrong

Using it on unsorted data.
Off-by-one errors and infinite loops.
Not defining whether boundaries are inclusive or half-open.

HOW TO EXPLAIN IT IN AN INTERVIEW

A professional answer shape

Say the invariant: if the target exists, it is inside the current search interval. Then explain how each comparison preserves that invariant while halving the interval.

Problem→Core idea→Invariant / state→Big-O→Trade-off

QUICK INTERVIEW CHECK

What problem does Binary Search solve?

Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.

What should I mention about complexity?

Its typical cost here is O(log n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

What is the most common mistake?

Using it on unsorted data.

Continue readingSorted arraysLower/upper boundBinary search on answer

function binarySearch(items, target) { let left = 0; let right = items.length - 1; while (left <= right) { const mid = left + Math.floor((right - left) / 2); if (items[mid] === target) return mid; if (items[mid] < target) left = mid + 1; else right = mid - 1; } return -1; }